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3 Answers
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Mr Giles' phrasebook uses -r, the same as Pinyin. The phrasebook was published after he created the Wade-Giles system, so presumably it uses this system.

(EDIT: I previously said "I think this might have been before the Wade-Giles system was formalized", but then found that the date of publication was 1901, while Wikipedia says Wade-Giles "was given completed form with Herbert Giles' Chinese–English dictionary of 1892")

This is not a complete answer, but the Wade-Giles example chart on this Chinese-language Wikipedia entry includes "kêrh" as a transcription of the rhotacized "哥儿." I do not know the general rule.

The GR (Gwoyeu Romatzyh) transcription system, which was used officially in China from 1928-1958, has complex rules for 儿化 spellings. I can't find a complete chart online, but, again, Chinese Wikipedia has some details. GR uses "l" to represent rhotacization, but the precise rules for how the resulting work is spelled differ depending on the syllable final and tone.

兒化 is the process of adding a 兒 at the end of words in some Notĥern Chinese dialects like the Beijing's one. There is no specific transcription for that other than adding a "r" in pinyin and a "ㄦ" in Zhuyin Fuhao. Although, in Taiwan, it's almost never seen since people don't do 兒化…